A Improved Logistic Chaotic Map and Its Application to Image Encryption and Hiding
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摘要: 鉴于原Logistic映射的映射范围有限、混沌参数范围小、分布不均匀等缺陷，该文提出一个新的改进型Logistic混沌映射。该映射有
$ \mu $ 和$ \alpha $ 两个参数，$ {x_{n - 1}} $ 和$ {x_n} $ 两个初值，参数和初值选取范围可扩展到任意实数，其混沌映射均为满映射，且映射范围可任意调控。将该映射应用到图像加密，其算法采用像素值异或(XOR)加密、像素位置置乱处理。之后再把密文数据隐藏在与密文无关的载图之中。对密文图像做了一系列的分析，包括图像的相邻像素点相关性，直方图分析和密钥敏感性测试。分析结果表明，所提加密算法具有很好的安全性和加密效果。-
关键词:
- Logistic混沌映射 /
- 图像加密 /
- 图像隐藏
Abstract: In view of the limited mapping range of the original Logistic map, the small range of chaotic parameters, and the uneven distribution, a new improved Logistic chaotic map is proposed. The mapping has two parameters$ \mu $ and$ \alpha $ , and two initial values of$ {x_{n - 1}} $ and$ {x_n} $ . The parameter and initial value selection range can be extended to any real number. The chaotic mapping is full mapping, and the mapping range can be adjusted arbitrarily. This mapping is applied to image encryption, and the algorithm uses pixel value Exclusive OR(XOR) encryption and pixel position is scrambled . Afterwards, the ciphertext data is hidden in the image that has nothing to do with the ciphertext. A series of analysis is done on the ciphertext image, including the correlation between adjacent pixels of the image, histogram analysis and key sensitivity test. The analysis result shows that the proposed encryption algorithm has good security and encryption effect.-
Key words:
- Logistic chaotic map /
- Image encryption /
- Image hiding
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表 1 Logistic映射与改进的Logistic映射比较
映射范围 初值取值范围 参数µ取值范围 原Logistic映射 [0,1] [0,1] (0,4] 改进的Logistic映射 任意实数 任意实数 任意实数 
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表 3 密钥敏感性分析(%)
NPCR UACI 只改变$ {x_{n - 1}} $ 99.5468 33.5983 只改变$ {x_n} $ 99.5692 33.6474 只改变$ \mu $ 99.5796 33.6091
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表 4 明文敏感性分析(%)
NPCR UACI 像素点1 99.5724 33.6345 像素点2 99.5716 33.6354 像素点3 99.5728 33.6357 平均值 99.5723 33.6352
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